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/* nrlin.c ****************************************************************
NR Library Package - Definitions and Linear Algebra Functions
James Trevelyan, University of Western Australia
Revision 2 January 1996
**************************************************************************/
#include <stdio.h>
#include <stddef.h>
#include <stdlib.h>
#include <math.h>
#ifdef __TURBOC__
#include <conio.h>
#endif
#include "nrlin.h"
/* Validity checking - use V_CHECK */
#define V_CHECK
/* Keep track of memory used - only for dmatrix and dvector calls at the moment */
static long mem_t = 0;
static int mats = 0;
static int dmats = 0;
static int vecs = 0;
static int dvecs = 0;
void using_mem( long space )
{
mem_t += space;
}
long mem_used( void )
{
return (mem_t);
}
void reportmemory( FILE *outfile )
{
fprintf( outfile, "Memory: %ld bytes\n", mem_t);
fprintf( outfile, "%d dmatrices, %d dvectors, %d matrices, %d vectors\n",
dmats, dvecs, mats, vecs );
}
void choldc(float **a, int n, float p[])
{
nrerror("Obtain \"choldc\" source from NR diskette");
}
void cholsl(float **a, int n, float p[], float b[], float x[])
{
nrerror("Obtain \"cholsl\" source from NR diskette");
}
void lubksb(float **a, int n, int *indx, float b[])
{
nrerror("Obtain \"lubksb\" source from NR diskette");
}
void ludcmp(float **a, int n, int *indx, float *d)
{
nrerror("Obtain \"ludcmp\" source from NR diskette");
}
void dcholdc(double **a, int n, double p[])
{
nrerror("Obtain \"choldc\" source from NR diskette");
}
void dcholsl(double **a, int n, double p[], double b[], double x[])
{
nrerror("Obtain \"cholsl\" source from NR diskette");
}
void dlubksb(double **a, int n, int *indx, double b[])
{
nrerror("Obtain \"lubksb\" source from NR diskette");
}
void dludcmp(double **a, int n, int *indx, double *d)
{
nrerror("Obtain \"ludcmp\" source from NR diskette");
}
#define NR_END 1
#define NR_TEST 1
#define FREE_ARG char*
static int alt_handler_defined = 0;
static void (*alt_error_handler)(char error_text[]);
void nrerror(char error_text[])
/* Numerical Recipes standard error handler */
{
if (alt_handler_defined) {
(*alt_error_handler)(error_text);
}
else {
fprintf(stderr,"Numerical Recipes run-time error...\n");
fprintf(stderr,"%s\n",error_text);
fprintf(stderr,"Press <ENTER> to return to system...");
getchar();
exit(1);
}
}
void nrerror_handler( void(*handler)(char error_text[]) )
{
alt_handler_defined = 1;
alt_error_handler = handler;
}
float *vector(I_ARG_T nl, I_ARG_T nh)
/* allocate a float vector with subscript range v[nl..nh] */
{
float *v;
v=(float *)malloc((size_t) ((nh-nl+1+NR_END+NR_TEST)*sizeof(float)));
using_mem( (nh-nl+1+NR_END+NR_TEST)*sizeof(float) );
if (!v) nrerror("allocation failure in dvector()");
v -= nl;
v += NR_END;
v[nl-1] = -322.0;
v[nh+1] = -722.0;
vecs++;
return (v);
}
int *ivector(I_ARG_T nl, I_ARG_T nh)
/* allocate an int vector with subscript range v[nl..nh] */
{
int *v;
v=(int *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(int)));
if (!v) nrerror("allocation failure in ivector()");
return v-nl+NR_END;
}
unsigned char *cvector(I_ARG_T nl, I_ARG_T nh)
/* allocate an unsigned char vector with subscript range v[nl..nh] */
{
unsigned char *v;
v=(unsigned char *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(unsigned char)));
if (!v) nrerror("allocation failure in cvector()");
return v-nl+NR_END;
}
long *lvector(I_ARG_T nl, I_ARG_T nh)
/* allocate an unsigned long vector with subscript range v[nl..nh] */
{
long *v;
v=(long *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(long)));
if (!v) nrerror("allocation failure in lvector()");
return v-nl+NR_END;
}
void flag_dvector( double *v, I_ARG_T nh)
{
v[0] = -322.0;
v[nh+1] = -722.0;
}
double *dvector(I_ARG_T nl, I_ARG_T nh)
/* allocate a double vector with subscript range v[nl..nh] */
{
double *v;
v=(double *)malloc((size_t) ((nh-nl+1+NR_END+NR_TEST)*sizeof(double)));
using_mem( (nh-nl+1+NR_END+NR_TEST)*sizeof(double) );
if (!v) nrerror("allocation failure in dvector()");
v -= nl;
v += NR_END;
v[nl-1] = -322.0;
v[nh+1] = -722.0;
dvecs++;
return (v);
}
float **matrix(I_ARG_T nrl, I_ARG_T nrh, I_ARG_T ncl, I_ARG_T nch)
/* allocate a float matrix with subscript range m[nrl..nrh][ncl..nch] */
{
I_ARG_T i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
float **m;
/* allocate pointers to rows */
m=(float **) malloc((size_t)((nrow+NR_END+1)*sizeof(float*)));
using_mem( (nrow+NR_END+1)*sizeof(float*) );
if (!m) nrerror("allocation failure 1 in matrix()");
m += NR_END + 1;
m -= nrl;
/* allocate rows and set pointers to them */
m[nrl]=(float *) malloc((size_t)((nrow*ncol+NR_END+NR_TEST)*sizeof(float)));
using_mem( (nrow*ncol+NR_END+NR_TEST)*sizeof(float) );
if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
m[nrl] += NR_END;
m[nrl] -= ncl;
m[nrl-2] = (float *)0x555;
m[nrl-1] = m[nrl]; /* covers m[0][0] mistake */
for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;
m[nrl][0]=-422.0;
m[nrh][nch+1]=-822.0;
/* return pointer to array of pointers to rows */
mats++;
return m;
}
/****************************************************************************/
/* double **dmatrix(I_ARG_T nrl, I_ARG_T nrh, I_ARG_T ncl, I_ARG_T nch)
Purpose:
allocate memory for a double matrix
with subscript range m[nrl..nrh][ncl..nch]
****************************************************************************/
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double **dmatrix(I_ARG_T nrl, I_ARG_T nrh, I_ARG_T ncl, I_ARG_T nch)
{
I_ARG_T i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
double **m;
/* allocate pointers to rows */
m=(double **) malloc((size_t)((nrow+NR_END+1)*sizeof(double*)));
using_mem( (nrow+NR_END+1)*sizeof(double*) );
if (!m) nrerror("allocation failure 1 in matrix()");
m += NR_END + 1;
m -= nrl;
/* allocate rows and set pointers to them */
m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END+NR_TEST)*sizeof(double)));
using_mem( (nrow*ncol+NR_END+NR_TEST)*sizeof(double) );
if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
m[nrl] += NR_END;
m[nrl] -= ncl;
m[nrl-2] = (double *)0x555;
m[nrl-1] = m[nrl]; /* covers m[0][0] mistake */
for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;
m[nrl][0]=-422.0;
m[nrh][nch+1]=-822.0;
/* return pointer to array of pointers to rows */
dmats++;
return m;
}
int **imatrix(I_ARG_T nrl, I_ARG_T nrh, I_ARG_T ncl, I_ARG_T nch)
/* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */
{
I_ARG_T i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
int **m;
/* allocate pointers to rows */
m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));
if (!m) nrerror("allocation failure 1 in matrix()");
m += NR_END;
m -= nrl;
/* allocate rows and set pointers to them */
m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END+NR_TEST)*sizeof(int)));
if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
m[nrl] += NR_END;
m[nrl] -= ncl;
for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;
/* return pointer to array of pointers to rows */
return m;
}
float **submatrix(float **a, I_ARG_T oldrl, I_ARG_T oldrh, I_ARG_T oldcl, I_ARG_T oldch,
I_ARG_T newrl, I_ARG_T newcl)
/* point a submatrix [newrl..][newcl..] to a[oldrl..oldrh][oldcl..oldch] */
{
I_ARG_T i,j,nrow=oldrh-oldrl+1,ncol=oldcl-newcl;
float **m;
/* allocate array of pointers to rows */
m=(float **) malloc((size_t) ((nrow+NR_END)*sizeof(float*)));
if (!m) nrerror("allocation failure in submatrix()");
m += NR_END;
m -= newrl;
/* set pointers to rows */
for(i=oldrl,j=newrl;i<=oldrh;i++,j++) m[j]=a[i]+ncol;
/* return pointer to array of pointers to rows */
return m;
}
float **convert_matrix(float *a, I_ARG_T nrl, I_ARG_T nrh, I_ARG_T ncl, I_ARG_T nch)
/* allocate a float matrix m[nrl..nrh][ncl..nch] that points to the matrix
declared in the standard C manner as a[nrow][ncol], where nrow=nrh-nrl+1
and ncol=nch-ncl+1. The routine should be called with the address
&a[0][0] as the first argument. */
{
I_ARG_T i,j,nrow=nrh-nrl+1,ncol=nch-ncl+1;
float **m;
/* allocate pointers to rows */
m=(float **) malloc((size_t) ((nrow+NR_END)*sizeof(float*)));
if (!m) nrerror("allocation failure in convert_matrix()");
m += NR_END;
m -= nrl;
/* set pointers to rows */
m[nrl]=a-ncl;
for(i=1,j=nrl+1;i<nrow;i++,j++) m[j]=m[j-1]+ncol;
/* return pointer to array of pointers to rows */
return m;
}
float ***f3tensor(I_ARG_T nrl, I_ARG_T nrh, I_ARG_T ncl, I_ARG_T nch, I_ARG_T ndl, I_ARG_T ndh)
/* allocate a float 3tensor with range t[nrl..nrh][ncl..nch][ndl..ndh] */
{
I_ARG_T i,j,nrow=nrh-nrl+1,ncol=nch-ncl+1,ndep=ndh-ndl+1;
float ***t;
/* allocate pointers to pointers to rows */
t=(float ***) malloc((size_t)((nrow+NR_END)*sizeof(float**)));
if (!t) nrerror("allocation failure 1 in f3tensor()");
t += NR_END;
t -= nrl;
/* allocate pointers to rows and set pointers to them */
t[nrl]=(float **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(float*)));
if (!t[nrl]) nrerror("allocation failure 2 in f3tensor()");
t[nrl] += NR_END;
t[nrl] -= ncl;
/* allocate rows and set pointers to them */
t[nrl][ncl]=(float *) malloc((size_t)((nrow*ncol*ndep+NR_END)*sizeof(float)));
if (!t[nrl][ncl]) nrerror("allocation failure 3 in f3tensor()");
t[nrl][ncl] += NR_END;
t[nrl][ncl] -= ndl;
for(j=ncl+1;j<=nch;j++) t[nrl][j]=t[nrl][j-1]+ndep;
for(i=nrl+1;i<=nrh;i++) {
t[i]=t[i-1]+ncol;
t[i][ncl]=t[i-1][ncl]+ncol*ndep;
for(j=ncl+1;j<=nch;j++) t[i][j]=t[i][j-1]+ndep;
}
/* return pointer to array of pointers to rows */
return t;
}
void free_vector(float *v, I_ARG_T nl, I_ARG_T nh)
/* free a float vector allocated with vector() */
{
if ( valid_vector( v, nl, nh ) ) {
free((FREE_ARG) (v+nl-NR_END));
using_mem( -(nh-nl+1+NR_END+NR_TEST)*sizeof(float) );
vecs--;
}
else
nrerror("Invalid vector pointer: free_vector");
}
void free_ivector(int *v, I_ARG_T nl, I_ARG_T nh)
/* free an int vector allocated with ivector() */
{
free((FREE_ARG) (v+nl-NR_END));
}
void free_cvector(unsigned char *v, I_ARG_T nl, I_ARG_T nh)
/* free an unsigned char vector allocated with cvector() */
{
free((FREE_ARG) (v+nl-NR_END));
}
void free_lvector(long *v, I_ARG_T nl, I_ARG_T nh)
/* free an unsigned long vector allocated with lvector() */
{
free((FREE_ARG) (v+nl-NR_END));
}
void free_dvector(double *v, I_ARG_T nl, I_ARG_T nh)
/* free a double vector allocated with dvector() */
{
if ( valid_dvector( v, nl, nh ) ) {
free((FREE_ARG) (v+nl-NR_END));
using_mem( -(long)(nh-nl+1+NR_END+NR_TEST)*sizeof(double) );
dvecs--;
}
else
nrerror("Invalid vector pointer: free_vector");
}
void free_matrix(float **m, I_ARG_T nrl, I_ARG_T nrh, I_ARG_T ncl, I_ARG_T nch)
/* free a float matrix allocated by matrix() */
{
I_ARG_T i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
if ( valid_matrix( m, nrl, nrh, ncl, nch ) ) {
m[nrl][ncl-1] = 0.0;
m[nrh][nch+1] = 0.0;
*(m-1) = (float *)NULL;
free((FREE_ARG) (m[nrl]+ncl-NR_END));
free((FREE_ARG) (m+nrl-NR_END-1));
using_mem(-(long)(nrow+NR_END+1)*sizeof(float*) );
using_mem(-(long)(nrow*ncol+NR_END+NR_TEST)*sizeof(float) );
mats--;
}
else {
nrerror("Invalid pointer to matrix: free_matrix");
}
}
void free_dmatrix(double **m, I_ARG_T nrl, I_ARG_T nrh, I_ARG_T ncl, I_ARG_T nch)
/* free a double matrix allocated by dmatrix() */
{
I_ARG_T i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
if ( valid_dmatrix( m, nrl, nrh, ncl, nch ) ) {
m[nrl][ncl-1] = 0.0;
m[nrh][nch+1] = 0.0;
*(m-1) = (double *)NULL;
free((FREE_ARG) (m[nrl]+ncl-NR_END));
free((FREE_ARG) (m+nrl-NR_END-1));
using_mem(-(long)(nrow+NR_END+1)*sizeof(double*) );
using_mem(-(long)(nrow*ncol+NR_END+NR_TEST)*sizeof(double) );
dmats--;
}
else {
nrerror("Invalid pointer to dmatrix: free_dmatrix");
}
}
void free_imatrix(int **m, I_ARG_T nrl, I_ARG_T nrh, I_ARG_T ncl, I_ARG_T nch)
/* free an int matrix allocated by imatrix() */
{
free((FREE_ARG) (m[nrl]+ncl-NR_END));
free((FREE_ARG) (m+nrl-NR_END));
}
void free_submatrix(float **b, I_ARG_T nrl, I_ARG_T nrh, I_ARG_T ncl, I_ARG_T nch)
/* free a submatrix allocated by submatrix() */
{
free((FREE_ARG) (b+nrl-NR_END));
}
void free_convert_matrix(float **b, I_ARG_T nrl, I_ARG_T nrh, I_ARG_T ncl, I_ARG_T nch)
/* free a matrix allocated by convert_matrix() */
{
free((FREE_ARG) (b+nrl-NR_END));
}
void free_f3tensor(float ***t, I_ARG_T nrl, I_ARG_T nrh, I_ARG_T ncl, I_ARG_T nch,
I_ARG_T ndl, I_ARG_T sndh)
/* free a float f3tensor allocated by f3tensor() */
{
free((FREE_ARG) (t[nrl][ncl]+ndl-NR_END));
free((FREE_ARG) (t[nrl]+ncl-NR_END));
free((FREE_ARG) (t+nrl-NR_END));
}
/* matrix inversion ref - Page 48 */
/****************************************************************************/
/* void dinverse( double **a, int n, double **y )
Purpose:
Find inverse of 'a' (decomposed in process!) and return as 'y'
****************************************************************************/
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void dinverse( double **a, int n, double **y )
{
double d, *col;
int i, j, *indx /* integer vector */;
#ifdef V_CHECK
if ( !valid_dmatrix_b( a ) )
nrerror("Invalid input matrix: dinverse");
if ( !valid_dmatrix_b( y ) )
nrerror("Invalid output matrix: dinverse");
#endif
indx = ivector( 1, n );
col = dvector( 1, n );
dludcmp( a, n, indx, &d);
for ( j=1; j<=n; j++ ) {
for ( i=1; i<=n; i++ ) col[i] = 0.0;
col[j] = 1.0;
dlubksb( a, n, indx, col );
for ( i=1; i<=n; i++ ) y[i][j] = col[i];
}
free_ivector( indx, 1, n );
free_dvector( col, 1, n );
}
/* if intending to compute inverse(A) * B, use columns of B in 'col' above instead
of unit vectors as shown - more accurate and faster */
void dinverse_mult( double **a, int a_rows, double **b, int b_cols, double **y )
/* Find inverse of 'a' (decomposed in process!) times 'b' and return result as 'y' */
{
double d, *col;
int i, j, *indx /* integer vector */;
#ifdef V_CHECK
if ( !valid_dmatrix_b( a ) )
nrerror("Invalid input matrix: dinverse_mult");
if ( !valid_dmatrix_b( b ) )
nrerror("Invalid output matrix: dinverse_mult");
if ( !valid_dmatrix_b( y ) )
nrerror("Invalid output matrix: dinverse_mult");
#endif
indx = ivector( 1, a_rows );
col = dvector( 1, a_rows );
dludcmp( a, a_rows, indx, &d);
for ( j=1; j<=b_cols; j++ ) {
for ( i=1; i<=a_rows; i++ ) col[i] = b[i][j];
dlubksb( a, a_rows, indx, col );
for ( i=1; i<=a_rows; i++ ) y[i][j] = col[i];
}
free_ivector( indx, 1, a_rows );
free_dvector( col, 1, a_rows );
}
/* positive definite symmetric matrix inversion ref - Page 97, 98 */
void dPDSinverse( double **a, int n, double **y )
/* Find inverse of 'a' (decomposed in process!) and return as 'y' */
{
double sum, *p, *col, *yr;
int i, j;
#ifdef V_CHECK
if ( !valid_dmatrix_b( a ) )
nrerror("Invalid input matrix: dPDSinverse");
if ( !valid_dmatrix_b( y ) )
nrerror("Invalid output matrix: dPDSinverse");
#endif
p = dvector( 1, n );
col = dvector( 1, n );
yr = dvector( 1, n );
dcholdc( a, n, p);
for ( j=1; j<=n; j++ ) {
for ( i=1; i<=n; i++ ) col[i] = 0.0;
col[j] = 1.0;
dcholsl( a, n, p, col, yr );
for ( i=1; i<=n; i++ ) y[i][j] = yr[i];
}
free_dvector( yr, 1, n );
free_dvector( col, 1, n );
free_dvector( p, 1, n );
}
void dPDS_L_inverse( double **a, int n, double **y )
/* Find inverse of L (decomposed a) and return as 'y' */
{
double sum, *p;
int i, j, k;
#ifdef V_CHECK
if ( !valid_dmatrix_b( a) )
nrerror("Invalid input matrix: dPDS_L_inverse");
if ( !valid_dmatrix_b( y ) )
nrerror("Invalid output matrix: dPDS_L_inverse");
#endif
p = dvector( 1, n );
dcholdc( a, n, p);
for ( i=1; i<=n; i++ ) {
a[i][i] = 1.0/p[i];
for ( j=i+1; j<=n; j++ ) {
sum = 0.0;
for (k=i; k<j; k++) sum -= a[j][k]*a[k][i];
a[j][i] = sum/p[j];
}
}
free_dvector( p, 1, n );
}